# How do you solve: sin(sin^-1 (0.9))?

I'm going to assume that by ${\sin}^{- 1}$ what is intended is what is also called the $\arcsin$ (the inverse of the $\sin$ function) and not the value of the $\sin$ function to the exponent of $- 1$.
$\sin \left(\arcsin \left(0.9\right)\right) = 0.9$
If you intended the $\left(- 1\right)$ to be an exponent then I know of no way to solve this other than to look-up the (approximated) values using a table of $\sin$ values or a calculator.